Vth using Node 
In using Node 
Rth or Rn 
Finding Rth using source injection and node 
Here is the mupad/matlab code that generates the answer Rth = 6.0591 ohms.
Comparing Node with Thevenin Equivalent 
Solving the node equations yields:
Using the Thevenin equivalent (and voltage divider) to compute voltage across the 12 ohm resistor:
So they match ...
Thevenin voltage and resistance can not be computed from a node analysis of the entire circuit, but the node analysis of the entire circuit can be used to check if the thevenin equivalent produces the same numbers.